Re: corrupting the youth

[Jack Uretsky <jlu@HEP.ANL.GOV>]

On Sun, 1 Sep 2002, John S. Denker wrote:

> paul o johnson wrote:
> > If Clifford Algebra is the mother's milk you say it is, why don't they teach
> > it in high school and college? I never heard of it until this thread
> > started.
>
> 0) I never heard of it either.  Basically I have no idea
> why it hasn't gotten more notice.
>
> 1) Leigh Palmer actually mentioned it in this forum six
> years ago (September 1996).
>
> 2) David Hestenes has some remarks on the history (including
> a fancy diagram) at
>   http://modelingnts.la.asu.edu/html/Evolution.html
> but doesn't explain why it hibernated for decades before
> the 1960s.
>
> 3) Some useful links and remarks can be found at
>   http://www.helsinki.fi/~lounesto/
>
> 4) Timothy Havel has a few interesting things to say about
> the history and the math:
>   http://mrix4.mit.edu/iap00_index.html
>   http://mrix4.mit.edu/IAP-00/lect0.pdf
>
> 5) There's always google:
>
> http://www.google.com/search?q=clifford-algebra+OR+geometric-algebra+history
>
> =====================
>
> BTW ... I made web pages out of the recent notes on scientific methods
> and on area of parallelograms / volume of parallelepipeds.
>   http://www.monmouth.com/~jsd/physics/scientific-methods.htm
>   http://www.monmouth.com/~jsd/physics/area-volume.htm
>
> ==================
>
> Jack Uretsky wrote:
>
> >  A/\B and AxB are one and the same animal.
>
> No, they are not.  They are closely related, but as I
> pointed out before, it would be unwise to replace the
> triple scalar product AxB.C with A/\B.C ... the proper
> scalar volume is ||A/\B/\C||.
>
> > possibility.... that the Clifford algebra approach
> > offers no new insights.
>
> I guarantee that those who don't bother to understand it
> won't get any new insights from it.
>
> As for me, I have already achieved one new insight, namely
> that the Maxwell equations work just fine in two spatial
> dimensions (plus time) ... provided they are properly
> written, without nasty cross products.  This insight came
> to me unbidden -- it was the answer to a question that I
> hadn't ever asked.  But there it was:  a solution not
> involving the 3rd spatial dimension, just sitting there
> staring up at me.  This insight won't go down in history
> alongside the invention of indoor plumbing, but it is
> more than sufficient to disprove the hypothesis that no
> new insights are offered.

        Please share your insight.  I lay a loop of wire carrying
current on a table.  A magnetized needle is placed inside the loop.  This
is all in two dimensions.  Now make a picture, without invoking a third
dimension, of the forces and/or torques acting on the needle.
                                        Regards,
                                                Jack

--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do.  Tonight it is only you and me, fish.
It is your strength against my intelligence.  It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
                     Greg Nagan from "The Old Man and the Sea" in
                     <The 5-MINUTE ILIAD and Other Classics>